Mixed norm estimates for some averaging operators in ℝ²

Daniel M. Oberlin

Vol. 223 (2006), No. 2, 349–360

DOI: 10.2140/pjm.2006.223.349

Abstract

We obtain mixed norm estimates for averaging operators on ℝ² defined by convolution with μ, where either μ is arclength measure on certain curves in ℝ² or dμ = dx∕x^β on the positive x-axis.

Keywords

mixed norm, averaging operator

Mathematical Subject Classification 2000

Primary: 42B20

Milestones

Received: 5 May 2004

Revised: 30 November 2004

Accepted: 30 December 2004

Published: 1 February 2006